Finance refers to monetary resources and to the study and
discipline
Discipline is the self-control that is gained by requiring that rules or orders be obeyed, and the ability to keep working at something that is difficult. Disciplinarians believe that such self-control is of the utmost importance and enforce a ...
of
money,
currency
A currency is a standardization of money in any form, in use or circulation as a medium of exchange, for example banknotes and coins. A more general definition is that a currency is a ''system of money'' in common use within a specific envi ...
,
assets and
liabilities. As a subject of study, is a field of
Business Administration
Business administration is the administration of a commercial enterprise. It includes all aspects of overseeing and supervising the business operations of an organization.
Overview
The administration of a business includes the performance o ...
wich study the planning, organizing, leading, and controlling of an organization's resources to achieve its goals. Based on the scope of financial activities in
financial systems, the discipline can be divided into
personal,
corporate
A corporation or body corporate is an individual or a group of people, such as an association or company, that has been authorized by the state to act as a single entity (a legal entity recognized by private and public law as "born out of s ...
, and
public finance.
In these financial systems, assets are bought, sold, or traded as
financial instrument
Financial instruments are monetary contracts between parties. They can be created, traded, modified and settled. They can be cash (currency), evidence of an ownership, interest in an entity or a contractual right to receive or deliver in the form ...
s, such as
currencies,
loan
In finance, a loan is the tender of money by one party to another with an agreement to pay it back. The recipient, or borrower, incurs a debt and is usually required to pay interest for the use of the money.
The document evidencing the deb ...
s,
bonds,
shares,
stocks,
options,
futures, etc. Assets can also be
bank
A bank is a financial institution that accepts Deposit account, deposits from the public and creates a demand deposit while simultaneously making loans. Lending activities can be directly performed by the bank or indirectly through capital m ...
ed,
invested, and
insured to maximize value and minimize loss. In practice,
risks are always present in any financial action and entities.
Due to its wide scope, a broad range of subfields exists within finance.
Asset-,
money-,
risk- and
investment management
Investment management (sometimes referred to more generally as financial asset management) is the professional asset management of various Security (finance), securities, including shareholdings, Bond (finance), bonds, and other assets, such as r ...
aim to maximize value and minimize
volatility.
Financial analysis
Financial analysis (also known as financial statement analysis, accounting analysis, or analysis of finance) refers to an assessment of the viability, stability, and profitability of a business, sub-business, project or investment.
It is per ...
assesses the viability, stability, and profitability of an action or entity. Some fields are multidisciplinary, such as
mathematical finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the financial field.
In general, there exist two separate branches of finance that req ...
,
financial law
Financial law is the law and regulation of the commercial banking, capital markets, insurance, derivatives and investment management sectors. Understanding financial law is crucial to appreciating the creation and formation of banking and finan ...
,
financial economics
Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on ''both sides'' of a trade".William F. Sharpe"Financial Economics", in
Its co ...
,
financial engineering and
financial technology. These fields are the foundation of
business
Business is the practice of making one's living or making money by producing or Trade, buying and selling Product (business), products (such as goods and Service (economics), services). It is also "any activity or enterprise entered into for ...
and
accounting
Accounting, also known as accountancy, is the process of recording and processing information about economic entity, economic entities, such as businesses and corporations. Accounting measures the results of an organization's economic activit ...
. In some cases,
theories in finance can be tested using the
scientific method
The scientific method is an Empirical evidence, empirical method for acquiring knowledge that has been referred to while doing science since at least the 17th century. Historically, it was developed through the centuries from the ancient and ...
, covered by
experimental finance.
The early history of finance parallels the early
history of money, which is
prehistoric. Ancient and medieval civilizations incorporated basic functions of finance, such as banking, trading and accounting, into their economies. In the late 19th century, the
global financial system was formed.
In the middle of the 20th century, finance emerged as a distinct academic discipline, separate from economics.
The earliest doctoral programs in finance were established in the 1960s and 1970s. Today, finance is also
widely studied through career-focused undergraduate and
master's level programs.
The financial system

As outlined, the financial system consists of the flows of capital that take place between individuals and households (
personal finance
Personal finance is the financial management that an individual or a family unit performs to budget, save, and spend monetary resources in a controlled manner, taking into account various financial risks and future life events.
When planni ...
), governments (
public finance), and businesses (
corporate finance
Corporate finance is an area of finance that deals with the sources of funding, and the capital structure of businesses, the actions that managers take to increase the Value investing, value of the firm to the shareholders, and the tools and analy ...
). "Finance" thus studies the process of channeling money from savers and investors to entities that need it. Savers and investors have money available which could earn interest or dividends if put to productive use. Individuals, companies and governments must obtain money from some external source, such as loans or credit, when they lack sufficient funds to run their operations.
In general, an entity whose income exceeds its
expenditure can lend or invest the excess, intending to earn a fair return. Correspondingly, an entity where income is less than expenditure can raise capital usually in one of two ways: (i) by borrowing in the form of a loan (private individuals), or by selling
government or corporate bonds; (ii) by a corporation selling
equity, also called stock or shares (which may take various forms:
preferred stock or
common stock). The owners of both bonds and stock may be
institutional investors—financial institutions such as investment banks and
pension funds—or private individuals, called
private investors or retail investors. (See
Financial market participants.)
The
lending is often indirect, through a
financial intermediary such as a
bank
A bank is a financial institution that accepts Deposit account, deposits from the public and creates a demand deposit while simultaneously making loans. Lending activities can be directly performed by the bank or indirectly through capital m ...
, or via the purchase of notes or
bonds (
corporate bonds,
government bond
A government bond or sovereign bond is a form of Bond (finance), bond issued by a government to support government spending, public spending. It generally includes a commitment to pay periodic interest, called Coupon (finance), coupon payments' ...
s, or mutual bonds) in the
bond market. The lender receives interest, the
borrower pays a higher interest than the lender receives, and the financial intermediary earns the difference for arranging the loan.
A bank aggregates the activities of many borrowers and lenders. Banks accept deposits from individuals and businesses, paying interest on these funds. The bank then lends these deposits to borrowers. Banks facilitate transactions between borrowers and lenders of various sizes, enabling efficient financial coordination.
Investing typically entails the purchase of
stock, either individual securities or via a
mutual fund
A mutual fund is an investment fund that pools money from many investors to purchase Security (finance), securities. The term is typically used in the United States, Canada, and India, while similar structures across the globe include the SICAV in ...
, for example. Stocks are usually sold by corporations to investors so as to raise required capital in the form of "
equity financing
In finance, equity is an ownership interest in property that may be subject to debts or other liabilities. Equity is measured for accounting purposes by subtracting liabilities from the value of the assets owned. For example, if someone owns ...
", as distinct from the debt financing described above. The financial intermediaries here are the
investment banks (which
find the initial investors and facilitate the listing of the securities, typically shares and bonds), the
securities exchanges (which allow their trade thereafter), and the various investment service providers (including
mutual funds,
pension funds,
wealth managers, and
stock brokers, typically servicing retail investors).
Inter-institutional trade and investment, and
fund-management at this scale, is referred to as "wholesale finance".
Institutions here
extend the products offered, with related trading, to include bespoke
options,
swaps, and
structured products, as well as
specialized financing; this "
financial engineering" is
inherently mathematical, and these institutions are then the major employers of
quantitative analysts (or "quants", see
below). In these institutions,
risk management,
regulatory capital, and
compliance play major roles.
Areas of finance
As outlined, finance comprises, broadly, the three areas of personal finance, corporate finance, and public finance. These, in turn, overlap and employ various activities and sub-disciplines—chiefly
investment
Investment is traditionally defined as the "commitment of resources into something expected to gain value over time". If an investment involves money, then it can be defined as a "commitment of money to receive more money later". From a broade ...
s, risk management, and
quantitative finance.
Personal finance

Personal finance refers to the practice of budgeting to ensure enough funds are available to meet basic needs, while ensuring there is only a reasonable level of risk to lose said capital. Personal finance may involve paying for education, financing
durable goods such as
real estate and cars, buying
insurance
Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to protect ...
, investing, and saving for
retirement. Personal finance may also involve paying for a loan or other debt obligations. The main areas of personal finance are considered to be income, spending, saving, investing, and protection. The following steps, as outlined by the Financial Planning Standards Board, suggest that an individual will understand a potentially secure personal finance plan after:
* Purchasing insurance to ensure protection against unforeseen personal events;
* Understanding the effects of tax policies, subsidies, or penalties on the management of personal finances;
* Understanding the effects of credit on individual financial standing;
* Developing a savings plan or financing for large purchases (auto, education, home);
* Planning a secure financial future in an environment of economic instability;
* Pursuing a checking or a savings account;
* Preparing for retirement or other long term expenses.
Corporate finance
Corporate finance deals with the actions that managers take to increase the value of the firm to the shareholders, the sources of funding and the
capital structure of corporations, and the tools and analysis used to allocate financial resources. While corporate finance is in principle different from
managerial finance, which studies the
financial management of all firms rather than corporations alone, the concepts are applicable to the financial problems of all firms,
[Pamela Drake and Frank Fabozzi (2009)]
What Is Finance?
and this area is then often referred to as "business finance".
Typically, "corporate finance" relates to the ''long term'' objective of maximizing the value of the
entity's assets, its
stock, and its
return to shareholders, while also
balancing risk and profitability. This entails three primary areas:
#
Capital budgeting: selecting which projects to invest in—here, accurately
determining value is crucial, as judgements about asset values can be "make or break".
#
Dividend policy: the use of "excess" funds—these are to be reinvested in the business or returned to shareholders.
#
Capital structure: deciding on the mix of funding to be used—here attempting to find the
optimal capital mix re debt-commitments vs
cost of capital. (This consists in understanding how much the firm has to generate
to satisfy investors, and by minimizing the
weighted average cost of capital (WACC) so that the value of the company increases.)
The latter
creates the link with
investment banking and
securities trading, as above, in that the capital raised will generically comprise debt, i.e.
corporate bonds, and
equity, often
listed shares. Re risk management within corporates, see
below.
Financial managers—i.e. as distinct from corporate financiers—focus more on the ''short term'' elements of profitability, cash flow, and "
working capital management" (
inventory
Inventory (British English) or stock (American English) is a quantity of the goods and materials that a business holds for the ultimate goal of resale, production or utilisation.
Inventory management is a discipline primarily about specifying ...
, credit and
debtors), which is concerned about the daily funding operations, and the goal is to maintain liquidity, minimize risk and maximize efficiency ensuring that the firm can
safely and profitably carry out its financial ''and operational'' objectives; i.e. that it: (1) can service both maturing short-term debt repayments, and scheduled long-term debt payments, and (2) has sufficient cash flow for ongoing and upcoming
operational expenses. (See
Financial management and
FP&A.)
Public finance

Public finance describes finance as related to sovereign states, sub-national entities, and related public entities or agencies. It generally encompasses a long-term strategic perspective regarding investment decisions that affect public entities. These long-term strategic periods typically encompass five or more years. Public finance is primarily concerned with:
* Identification of
required expenditures of a public sector entity;
* Source(s) of that
entity's revenue;
* The
budgeting process;
* Sovereign
debt issuance, or
municipal bonds for
public works
Public works are a broad category of infrastructure projects, financed and procured by a government body for recreational, employment, and health and safety uses in the greater community. They include public buildings ( municipal buildings, ...
projects.
Central banks, such as the
Federal Reserve System banks in the
United States
The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
and the
Bank of England
The Bank of England is the central bank of the United Kingdom and the model on which most modern central banks have been based. Established in 1694 to act as the Kingdom of England, English Government's banker and debt manager, and still one ...
in the
United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Northwestern Europe, off the coast of European mainland, the continental mainland. It comprises England, Scotlan ...
, are strong players in public finance. They act as
lenders of last resort as well as strong influences on monetary and credit conditions in the economy.
Development finance, which is related, concerns investment in
economic development
In economics, economic development (or economic and social development) is the process by which the economic well-being and quality of life of a nation, region, local community, or an individual are improved according to targeted goals and object ...
projects provided by a
(quasi) governmental institution on a non-commercial basis; these projects would otherwise not be able
to get financing. A
public–private partnership is primarily used for
infrastructure projects: a private sector corporate provides the financing up-front, and then draws profits from taxpayers or users.
Climate finance, and the related
Environmental finance, address the financial strategies, resources
and instruments used in
climate change mitigation.
Investment management

Investment management
is the professional asset management of various securities—typically shares and bonds, but also other assets, such as real estate, commodities and
alternative investments—in order to meet specified investment goals for the benefit of investors.
As above, investors may be institutions, such as insurance companies, pension funds, corporations, charities, educational establishments, or private investors, either directly via investment contracts or, more commonly, via collective investment schemes like mutual funds,
exchange-traded funds
An exchange-traded fund (ETF) is a type of investment fund that is also an exchange-traded product, i.e., it is traded on stock exchanges. ETFs own financial assets such as stocks, Bond (finance), bonds, currencies, debts, futures contracts, and ...
, or
real estate investment trusts.
At the heart of investment management
is
asset allocation—
diversifying the exposure among these
asset classes, and among individual securities within each asset class—as appropriate to the client's
investment policy, in turn, a function of risk profile, investment goals, and investment horizon (see
Investor profile). Here:
*
Portfolio optimization is the process of selecting the best portfolio given the client's objectives and constraints.
*
Fundamental analysis is the approach typically applied in
valuing and evaluating the individual securities.
*
Technical analysis is about forecasting future asset prices with past data.
Overlaid is the portfolio manager's
investment style—broadly,
active vs
passive,
value vs
growth, and
small cap vs.
large cap—and
investment strategy.
In a well-diversified portfolio, achieved
investment performance will, in general, largely be a function of the asset mix selected, while the individual securities are less impactful. The specific approach or philosophy will also be significant, depending on the extent to which it is complementary with the
market cycle.
Additional to this
diversification, the fundamental risk mitigant employed,
investment managers will apply various hedging techniques as appropriate,
these may relate to the
portfolio as a whole or
to individual stocks.
Bond portfolios are often (instead) managed via
cash flow matching or
immunization
Immunization, or immunisation, is the process by which an individual's immune system becomes fortified against an infectious agent (known as the antigen, immunogen). When this system is exposed to molecules that are foreign to the body, called ' ...
, while for derivative portfolios and positions, traders use
"the Greeks" to measure and then offset sensitivities. In parallel, managers –
active and
passive –
will monitor tracking error, thereby minimizing and preempting any underperformance
vs their "benchmark".
A
quantitative fund is managed using
computer-based mathematical techniques (increasingly,
machine learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task ( ...
) instead of human judgment. The actual trading
is typically automated via
sophisticated algorithms.
Risk management
Risk management, in general, is the study of how to control risks and balance the possibility of gains; it is the process of measuring risk and then developing and implementing strategies to manage that risk.
Financial risk management
Financial risk management is the practice of protecting Value (economics), economic value in a business, firm by managing exposure to financial risk - principally credit risk and market risk, with more specific variants as listed aside - as well ...
is the practice of protecting
corporate value against
financial risk
Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financi ...
s, often by
"hedging" exposure to these using financial instruments. The focus is particularly on credit and market risk, and in banks, through regulatory capital, includes operational risk.
*
Credit risk is the risk of
default on a debt that may arise from a borrower failing to make required payments;
*
Market risk relates to losses arising from movements in market variables such as prices and exchange rates;
*
Operational risk relates to failures in internal processes, people, and systems, or to external events (these risks will often be
insured).
Financial risk management is
related to corporate finance in two ways. Firstly, firm exposure to market risk is a direct result of previous capital investments and funding decisions; while credit risk arises from the business's credit policy and is often addressed through
credit insurance and
provisioning. Secondly, both disciplines share the goal of enhancing or at least preserving, the firm's
economic value, and in this context overlaps also
enterprise risk management, typically the domain of
strategic management. Here, businesses devote much time and effort to
forecasting,
analytics and
performance monitoring. (See
ALM and
treasury management.)
For banks and other wholesale institutions,
risk management
focuses on managing, and as necessary hedging, the various positions held by the institution—both
trading positions and
long term exposures—and on calculating and monitoring the resultant
economic capital, and
regulatory capital under
Basel III. The calculations here are mathematically sophisticated, and within the domain of
quantitative finance as below. Credit risk is inherent in the business of banking, but additionally, these institutions are exposed to
counterparty credit risk. Banks typically employ
Middle office "Risk Groups", whereas
front office risk teams provide risk "services" (or "solutions") to customers.
Insurers manage their own risks with a focus on
solvency and the ability to pay claims:
Life Insurers are concerned more with
longevity risk and
interest rate risk; Short-Term Insurers (
Property
Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, re ...
,
Health
Health has a variety of definitions, which have been used for different purposes over time. In general, it refers to physical and emotional well-being, especially that associated with normal functioning of the human body, absent of disease, p ...
,
Casualty) emphasize
catastrophe- and claims volatility risks. For expected claims
reserves are set aside periodically, while to absorb unexpected losses, a minimum
level of capital is maintained.
Quantitative finance

Quantitative finance—also referred to as "mathematical finance"—includes those finance activities where
a sophisticated mathematical model is required,
[See discussion here: ] and thus overlaps several of the above.
As a specialized practice area, quantitative finance comprises primarily three sub-disciplines; the underlying theory and techniques
are discussed in the next section:
# Quantitative finance is often synonymous with
financial engineering. This area generally underpins a bank's
customer-driven derivatives business—delivering bespoke
OTC-contracts and
"exotics", and
designing the various structured products and solutions mentioned—and encompasses
modeling and programming in support of the initial trade, and its subsequent hedging and management.
# Quantitative finance also significantly overlaps
financial risk management
Financial risk management is the practice of protecting Value (economics), economic value in a business, firm by managing exposure to financial risk - principally credit risk and market risk, with more specific variants as listed aside - as well ...
in banking, as
mentioned, both as regards this hedging, and as regards economic capital as well as compliance with regulations and
the Basel capital / liquidity requirements.
# "Quants" are also responsible for building and deploying the investment strategies at the quantitative funds
mentioned; they are also involved in
quantitative investing more generally, in areas such as
trading strategy formulation, and in
automated trading,
high-frequency trading,
algorithmic trading, and
program trading.
Financial theory
Financial theory is studied and developed within the disciplines of
management
Management (or managing) is the administration of organizations, whether businesses, nonprofit organizations, or a Government agency, government bodies through business administration, Nonprofit studies, nonprofit management, or the political s ...
,
(financial) economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
,
accountancy
Accounting, also known as accountancy, is the process of recording and processing information about economic entities, such as businesses and corporations. Accounting measures the results of an organization's economic activities and conveys ...
and
applied mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...
.
In the abstract,
''finance'' is concerned with the investment and deployment of
assets and
liabilities over "space and time"; i.e., it is about performing
valuation and
asset allocation today, based on the risk and uncertainty of future outcomes while appropriately incorporating the
time value of money.
Determining the
present value of these future values, "discounting", must be at the
risk-appropriate discount rate, in turn, a major focus of finance-theory.
["Finance"](_blank)
Farlex Financial Dictionary. 2012As financial theory has roots in many disciplines, including mathematics, statistics, economics, physics, and psychology, it can be considered a mix of an
art and
science
Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
,
[ and there are ongoing related efforts to organize a list of unsolved problems in finance.
]
Managerial finance
Managerial finance[What is managerial finance?](_blank)
, Corporate Finance Institute
is the branch of finance that deals with the financial aspects of the management
Management (or managing) is the administration of organizations, whether businesses, nonprofit organizations, or a Government agency, government bodies through business administration, Nonprofit studies, nonprofit management, or the political s ...
of a company, and the financial dimension of managerial decision-making more broadly. It provides the theoretical underpin for the practice described above, concerning itself with the managerial application of the various finance techniques. Academics working in this area are typically based in business school
A business school is a higher education institution or professional school that teaches courses leading to degrees in business administration or management. A business school may also be referred to as school of management, management school, s ...
finance departments, in accounting
Accounting, also known as accountancy, is the process of recording and processing information about economic entity, economic entities, such as businesses and corporations. Accounting measures the results of an organization's economic activit ...
, or in management science.
The tools addressed and developed relate in the main to managerial accounting and corporate finance
Corporate finance is an area of finance that deals with the sources of funding, and the capital structure of businesses, the actions that managers take to increase the Value investing, value of the firm to the shareholders, and the tools and analy ...
:
the former allow management to better understand, and hence act on, financial information relating to profitability and performance; the latter, as above, are about optimizing the overall financial structure, including its impact on working capital. Key aspects of managerial finance thus include:
# Financial planning and forecasting
# Capital budgeting
# Capital structure
# Working capital management
# Risk management
# Financial analysis and reporting.
The discussion, however, extends to business strategy more broadly, emphasizing alignment with the company's overall strategic objectives; and similarly incorporates the managerial perspectives of planning, directing, and controlling.
Financial economics
Financial economics[For an overview, se]
"Financial Economics"
, William F. Sharpe (Stanford University manuscript) is the branch of economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
that studies the interrelation of financial variables, such as prices, interest rate
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...
s and shares, as opposed to real economic variables, i.e. goods and services
Goods are items that are usually (but not always) tangible, such as pens or Apple, apples. Services are activities provided by other people, such as teachers or barbers. Taken together, it is the Production (economics), production, distributio ...
. It thus centers on pricing, decision making, and risk management in the financial markets, and produces many of the commonly employed financial models. ( Financial econometrics is the branch of financial economics that uses econometric techniques to parameterize the relationships suggested.)
The discipline has two main areas of focus:[See the discussion re finance theory by Fama and Miller under .] asset pricing
In financial economics, asset pricing refers to a formal treatment and development of two interrelated Price, pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, ...
and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital; respectively:
# Asset pricing theory develops the models used in determining the risk-appropriate discount rate, and in pricing derivatives; and includes the portfolio- and investment theory applied in asset management. The analysis essentially explores how rational investors would apply risk and return to the problem of investment
Investment is traditionally defined as the "commitment of resources into something expected to gain value over time". If an investment involves money, then it can be defined as a "commitment of money to receive more money later". From a broade ...
under uncertainty, producing the key " Fundamental theorem of asset pricing". Here, the twin assumptions of rationality and market efficiency lead to modern portfolio theory (the CAPM), and to the Black–Scholes theory for option valuation. At more advanced levels—and often in response to financial crises—the study then extends these "neoclassical" models to incorporate phenomena where their assumptions do not hold, or to more general settings.
# Much of corporate finance theory, by contrast, considers investment under " certainty" ( Fisher separation theorem, "theory of investment value", and Modigliani–Miller theorem). Here, theory and methods are developed for the decisioning about funding, dividends, and capital structure discussed above. A recent development is to incorporate uncertainty and contingency—and thus various elements of asset pricing—into these decisions, employing for example real options analysis.
Financial mathematics
Financial mathematics[Research Area: Financial Mathematics and Engineering](_blank)
, Society for Industrial and Applied Mathematics is the field of applied mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...
concerned with financial markets;
Louis Bachelier's doctoral thesis, defended in 1900, is considered to be the first scholarly work in this area. The field is largely focused on the modeling of derivatives—with much emphasis on interest rate- and credit risk modeling—while other important areas include insurance mathematics and quantitative portfolio management. Relatedly, the techniques developed are applied to pricing and hedging a wide range of asset-backed, government
A government is the system or group of people governing an organized community, generally a State (polity), state.
In the case of its broad associative definition, government normally consists of legislature, executive (government), execu ...
, and corporate
A corporation or body corporate is an individual or a group of people, such as an association or company, that has been authorized by the state to act as a single entity (a legal entity recognized by private and public law as "born out of s ...
-securities.
As above, in terms of practice, the field is referred to as quantitative finance and / or mathematical finance, and comprises primarily the three areas discussed.
The main mathematical tools and techniques are, correspondingly:
* for derivatives,[For a survey, se]
"Financial Models"
, from Michael Mastro (2013). ''Financial Derivative and Energy Market Valuation'', John Wiley & Sons. . Itô's stochastic calculus, simulation
A simulation is an imitative representation of a process or system that could exist in the real world. In this broad sense, simulation can often be used interchangeably with model. Sometimes a clear distinction between the two terms is made, in ...
, and partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.
The function is often thought of as an "unknown" that solves the equation, similar to ho ...
s; see aside boxed discussion re the prototypical Black-Scholes model and the various numeric techniques now applied
* for risk management,[See generally, Roy E. DeMeo (N.D.]
Quantitative Risk Management: VaR and Others
value at risk, stress testing and "sensitivities" analysis (applying the "greeks"); the underlying mathematics comprises mixture models, PCA, volatility clustering and copulas.
* in both of these areas, and particularly for portfolio problems, quants employ sophisticated optimization techniques
Mathematically, these separate into two analytic branches: derivatives pricing uses risk-neutral probability (or arbitrage-pricing probability), denoted by "Q"; while risk and portfolio management generally use physical (or actual or actuarial) probability, denoted by "P". These are interrelated through the above " Fundamental theorem of asset pricing".
The subject has a close relationship with financial economics, which, as outlined, is concerned with much of the underlying theory that is involved in financial mathematics: generally, financial mathematics will derive and extend the mathematical models suggested. Computational finance is the branch of (applied) computer science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...
that deals with problems of practical interest in finance, and especially emphasizes the numerical methods applied here.
Experimental finance
Experimental finance[Bloomfield, Robert and Anderson, Alyssa]
"Experimental finance"
. In Baker, H. Kent, and Nofsinger, John R., eds. Behavioral finance: investors, corporations, and markets. Vol. 6. John Wiley & Sons, 2010. pp. 113–131. aims to establish different market settings and environments to experimentally observe and provide a lens through which science can analyze agents' behavior and the resulting characteristics of trading flows, information diffusion, and aggregation, price setting mechanisms, and returns processes. Researchers in experimental finance can study to what extent existing financial economics theory makes valid predictions and therefore prove them, as well as attempt to discover new principles on which such theory can be extended and be applied to future financial decisions. Research may proceed by conducting trading simulations or by establishing and studying the behavior of people in artificial, competitive, market-like settings.
Behavioral finance
Behavioral finance studies how the ''psychology
Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ...
'' of investors or managers affects financial decisions and markets
and is relevant when making a decision that can impact either negatively or positively on one of their areas. With more in-depth research into behavioral finance, it is possible to bridge what actually happens in financial markets with analysis based on financial theory. Behavioral finance has grown over the last few decades to become an integral aspect of finance. Nowadays there is a need for more theory and testing of the effects of feelings on financial decisions. Especially, because now the time has come to move beyond behavioral finance to social finance, which studies the structure of social interactions, how financial ideas spread, and how social processes affect financial decisions and outcomes.
Behavioral finance includes such topics as:
# Empirical studies that demonstrate significant deviations from classical theories;
# Models of how psychology affects and impacts trading and prices;
# Forecasting based on these methods;
# Studies of experimental asset markets and the use of models to forecast experiments.
A strand of behavioral finance has been dubbed quantitative behavioral finance, which uses mathematical and statistical methodology to understand behavioral biases in conjunction with valuation.
Quantum finance
Quantum finance involves applying quantum mechanical approaches to financial theory, providing novel methods and perspectives in the field. ''Quantum'' ''finance'' is an interdisciplinary field, in which theories and methods developed by ''quantum'' physicists and economists are applied to solve financial problems. It represents a branch known as econophysics. Although ''quantum'' computational methods have been around for quite some time and use the basic principles of physics to better understand the ways to implement and manage cash flows, it is mathematics that is actually important in this new scenario Finance theory is heavily based on financial instrument
Financial instruments are monetary contracts between parties. They can be created, traded, modified and settled. They can be cash (currency), evidence of an ownership, interest in an entity or a contractual right to receive or deliver in the form ...
pricing such as stock option pricing. Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known as computational finance. Many computational finance problems have a high degree of computational complexity and are slow to converge to a solution on classical computers. In particular, when it comes to option pricing, there is additional complexity resulting from the need to respond to quickly changing markets. For example, in order to take advantage of inaccurately priced stock options, the computation must complete before the next change in the almost continuously changing stock market. As a result, the finance community is always looking for ways to overcome the resulting performance issues that arise when pricing options. This has led to research that applies alternative computing techniques to finance. Most commonly used quantum financial models are quantum continuous model, quantum binomial model, multi-step quantum binomial model etc.
History of finance
The origin of finance can be traced to the beginning of state formation and trade during the Bronze Age
The Bronze Age () was a historical period characterised principally by the use of bronze tools and the development of complex urban societies, as well as the adoption of writing in some areas. The Bronze Age is the middle principal period of ...
. The earliest historical evidence of finance is dated to around 3000 BCE. Banking originated in West Asia
West Asia (also called Western Asia or Southwest Asia) is the westernmost region of Asia. As defined by most academics, UN bodies and other institutions, the subregion consists of Anatolia, the Arabian Peninsula, Iran, Mesopotamia, the Armenian ...
, where temples and palaces were used as safe places for the storage of valuables. Initially, the only valuable that could be deposited was grain, but cattle and precious materials were eventually included. During the same period, the Sumerian city of Uruk
Uruk, the archeological site known today as Warka, was an ancient city in the Near East, located east of the current bed of the Euphrates River, on an ancient, now-dried channel of the river in Muthanna Governorate, Iraq. The site lies 93 kilo ...
in Mesopotamia
Mesopotamia is a historical region of West Asia situated within the Tigris–Euphrates river system, in the northern part of the Fertile Crescent. Today, Mesopotamia is known as present-day Iraq and forms the eastern geographic boundary of ...
supported trade by lending as well as the use of interest. In Sumerian, "interest" was ''mas'', which translates to "calf". In Greece
Greece, officially the Hellenic Republic, is a country in Southeast Europe. Located on the southern tip of the Balkan peninsula, it shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to th ...
and Egypt
Egypt ( , ), officially the Arab Republic of Egypt, is a country spanning the Northeast Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via the Sinai Peninsula. It is bordered by the Mediterranean Sea to northe ...
, the words used for interest, ''tokos'' and ''ms'' respectively, meant "to give birth". In these cultures, interest indicated a valuable increase, and seemed to consider it from the lender's point of view. The Code of Hammurabi (1792–1750 BCE) included laws governing banking operations. The Babylonians were accustomed to charging interest at the rate of 20 percent per year. By 1200 BCE, cowrie shells were used as a form of money in China
China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...
.
The use of coins as a means of representing money began in the years between 700 and 500 BCE. Herodotus mentions the use of crude coins in Lydia around 687 BCE and, by 640 BCE, the Lydians had started to use coin money more widely and opened permanent retail shops. Shortly after, cities in Classical Greece, such as Aegina, Athens
Athens ( ) is the Capital city, capital and List of cities and towns in Greece, largest city of Greece. A significant coastal urban area in the Mediterranean, Athens is also the capital of the Attica (region), Attica region and is the southe ...
, and Corinth, started minting their own coins between 595 and 570 BCE. During the Roman Republic
The Roman Republic ( ) was the era of Ancient Rome, classical Roman civilisation beginning with Overthrow of the Roman monarchy, the overthrow of the Roman Kingdom (traditionally dated to 509 BC) and ending in 27 BC with the establis ...
, interest was outlawed by the ''Lex Genucia'' reforms in 342 BCE, though the provision went largely unenforced. Under Julius Caesar
Gaius Julius Caesar (12 or 13 July 100 BC – 15 March 44 BC) was a Roman general and statesman. A member of the First Triumvirate, Caesar led the Roman armies in the Gallic Wars before defeating his political rival Pompey in Caesar's civil wa ...
, a ceiling on interest rates of 12% was set, and much later under Justinian
Justinian I (, ; 48214 November 565), also known as Justinian the Great, was Roman emperor from 527 to 565.
His reign was marked by the ambitious but only partly realized ''renovatio imperii'', or "restoration of the Empire". This ambition was ...
it was lowered even further to between 4% and 8%.
The first stock exchange was opened in Antwerp
Antwerp (; ; ) is a City status in Belgium, city and a Municipalities of Belgium, municipality in the Flemish Region of Belgium. It is the capital and largest city of Antwerp Province, and the third-largest city in Belgium by area at , after ...
in 1531. Since then, popular exchanges such as the London Stock Exchange (founded in 1773) and the New York Stock Exchange
The New York Stock Exchange (NYSE, nicknamed "The Big Board") is an American stock exchange in the Financial District, Manhattan, Financial District of Lower Manhattan in New York City. It is the List of stock exchanges, largest stock excha ...
(founded in 1793) were created.
See also
* 2008 financial crisis
* Outline of finance
Notes
References
Further reading
*
*
*
*
* Kiyosaki, Robert and Sharon Lechter (2000). '' Rich Dad Poor Dad: What the Rich Teach Their Kids About Money That the Poor and Middle Class Do Not!'' Warner Business Books.
*
*
*
External links
Hypertextual Finance Glossary
( Campbell Harvey)
Finance Glossary
( Pierre Vernimmen)
Glossary of financial risk management terms
( Risk.net)
Glossary of Key Investment Terms
(PIMCO
Pacific Investment Management Company LLC (PIMCO) is an American investment management firm. While it has a specific focus on active fixed income management worldwide, it manages investments in many asset classes, including fixed income, share ca ...
)
Corporate finance resources
( Aswath Damodaran)
Financial management resources
( James Van Horne)
Personal finance resources
( Financial Literacy and Education Commission, mymoney.gov)
Public finance resources
(Governance and Social Development Resource Centre, gsdrc.org) []
Risk management resources
(Global Risk Institute)
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